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The following program coded in fortran computes the 4 fringe field integrals I1, I2, I3 and I4
for either a magnetic or an electrostatic quadrupole. The necessary data are read in from a corresponding
data file.
PROGRAM FRINGE
C
C PROGRAM TO COMPUTE FRINGE FIELD INTEGRALS
C SEE NUCL. INST. AND METH. 103 (1972) P.117-124
C FIRST TIME COMPILED BY U. ROHRER (SIN), JULY 1986
C
CHARACTER*40 TITLE
REAL F(0:200), FF(0:200)
C
DO I = 0, 200
F(I) = 0.
ENDDO
C
C READ IN GRADIENT ON QUAD AXIS
C
READ(1,1001) TITLE
1001 FORMAT(A)
TYPE *,TITLE
READ(1,1002) DZ,AP ! INCREMENT IN Z AND APERTURE RADIUS
1002 FORMAT(2F10.1)
READ(1,1000) N1,N2
FMAX = FLOAT(N1 + N2) / 2.
F(200) = 1.
I = 199
C
10 READ(1,1000,END=20) N1,N2
1000 FORMAT(2I5)
F(I) = FLOAT(N1 + N2) / 2.
F(I) = F(I) / FMAX ! NORMALIZE
I = I - 1
GO TO 10
C
20 DZ = DZ / AP ! NORMALIZE (Z IS MEASURED IN UNITS OF AP)
C
C FF(Z) IS INTEGRAL OF F(I) ALONG Z ( AS FUNCTION OF Z)
C
FF(0) = 0.
DO I = 1, 200
FM = (F(I) + F(I-1)) / 2.
FF(I) = FF(I-1) + FM * DZ
ENDDO
C
ZB = FF(200) ! KIND OF AN OFFSET
C
C CONPUTE INTEGRAL I1
C
SUM = 0.
DO I = 1, 200
FFM = (FF(I) + FF(I-1)) / 2.
SUM = SUM + FFM * DZ
ENDDO
XI1 = SUM - 0.5 * ZB**2
TYPE *, 'I1 =',XI1
C
C CONPUTE INTEGRAL I2
C
SUM = 0.
Z = ZB - 200. * DZ + DZ/2.
DO I = 1, 200
FFM = (FF(I) + FF(I-1)) / 2.
SUM = SUM + Z * FFM * DZ
Z = Z + DZ
ENDDO
XI2 = SUM - ZB**3 / 3.
TYPE *, 'I2 =',XI2
C
C CONPUTE INTEGRAL I3
C
SUM = 0.
DO I = 1, 200
FFM = (FF(I) + FF(I-1)) / 2.
FFM2 = FFM**2
SUM = SUM + FFM2 * DZ
ENDDO
XI3 = SUM - ZB**3 / 3.
TYPE *, 'I3 =',XI3
C
C CONPUTE INTEGRAL I4
C
SUM = 0.
DO I = 1, 200
FFM = (F(I) + F(I-1)) / 2.
FFM2 = FFM**2
SUM = SUM + FFM2 * DZ
ENDDO
XI4 = SUM - ZB
TYPE *, 'I4 =',XI4
C
C FINISHED
C
CALL EXIT
END
Sample input file. Note that the enumeration of field values starts from the
interior of the quad (first value is the max). 2 rows are used, because field
measurements on the axis are done by taking data by moving in and out the measurement
device. The average of the 2 values should be taken for our purpose.
LINEAR AXIAL GRADIENT 2.,200. 1000 1000 1000 1000 1000 1000 1000 1000 990 990 980 980 970 970 960 960 .. .. .. .. 60 60 50 50 40 40 30 30 20 20 10 10 0 0 0 0 0 0 0 0
Last updated by
Urs Rohrer on 8-Feb-2006